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Multinomial Theorem

Combinatorics and Graph Theory

The multinomial theorem describes how to expand a power of a sum of several terms, generalizing the binomial theorem from two terms to any number of terms. For a sum of m terms raised to the nth power, it expresses the expansion as a sum of terms with multinomial coefficients of the form n factorial divided by the product of the factorials of the individual exponents, which must themselves sum to n, and the theorem reduces to the ordinary binomial theorem when m equals 2; it has applications in combinatorics, probability and polynomial algebra, including counting arrangements of objects into bins and permutations of words with repeated letters. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

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Source Multinomial theorem (Wikipedia)
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1. Multinomial theorem (Wikipedia)
  • Lead section
    In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum.
  • In Group: Enumerative, Additive and Algebraic Combinatorics, Lead
    In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum.
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